The original Pension act of 1908 required a person to have been a resident of the country for 25 years this also applied for disability pensions introduced in 1910, maternity allowance introduced in 1912, re-install that provision and your problem is solved.
The federal Government when introducing Unemployment benefits across the nation took a lot of taxes from the states to cover the cost of the pension, thus expanding substantially their revenue, little of which was actually used for the benefit, so give it back to the states.
